1. Field of the Invention
The present invention relates to a cup-shaped wave gear device having a high reduction ratio of 100 or higher, for example, and particularly relates to a wave gear device in which a diaphragm of a cup-shaped flexible external gear has a cross-sectional shape that is adapted for alleviating stress concentration.
2. Description of the Related Art
Known wave gear devices include a cup-shaped wave gear devices in which a flexible external gear thereof is cup-shaped. FIG. 1 is a longitudinal sectional view showing a typical cup-shaped wave gear device, and FIG. 2 is a block diagram showing the structure thereof in cross section in a plane perpendicular to a central axis of the device. As shown in these drawings, a cup-shaped wave gear device 1 is provided with an annular rigid internal gear 2, a cup-shaped flexible external gear 3 disposed in concentric fashion inside the internal gear, and an elliptically profiled wave generator 4 fitted inside the external gear. The flexible external gear 3 is provided with a flexible cylindrical body 11, an annular diaphragm 12 extending towards inside in a radial direction from one end in a central axis direction of the cylindrical body, a discoid rigid boss 13 made continuous with an internal peripheral edge of the diaphragm 12, and external teeth 14 formed in an external peripheral surface portion of the other end of the cylindrical body 11.
The portion of the cylindrical body 11 where the external teeth 14 are formed in the flexible external gear 3 thus shaped is flexed in an elliptical shape by the wave generator 4, and the external teeth positioned at both ends in a major axis direction of this ellipse mesh with internal teeth 15 of the rigid internal gear 2. Since the numbers of teeth in the gears 2 and 3 differ by 2n (n is a positive integer), meshing positions of the gears 2 and 3 move in a circumferential direction when the wave generator 4 is rotated by a motor or other rotational driving source, and relative rotation occurs in the gears 2 and 3 according to the difference in the number of gear teeth. The rigid internal gear 2 is generally fixed, and rotation having a considerably reduced speed is outputted from the flexible external gear 3.
The cylindrical body 11 of the cup-shaped flexible external gear 3 flexed in the elliptical shape by the wave generator 4 has a cylindrical shape in a state prior to being deformed, as shown in FIG. 3(a). After flexure into the elliptical shape by the wave generator 4, the cross-section that includes a major axis thereof reaches a state in which the cylindrical body 11 gradually widens outward in the direction from the side of the diaphragm 12 toward an open end 11a, as shown in FIG. 3(b). As shown in FIG. 3(c), the cross-section that includes a minor axis of the ellipse reaches a state in which the cylindrical body 11 gradually narrows in the direction from the side of the diaphragm 12 toward the open end 11a. 
The diaphragm 12 is formed between the cylindrical body 11 and the rigid boss 13 in order to flex the portion of the cylindrical body 11 on the side of the open end 11a into the elliptical shape. Specifically, when the open end 11a of the cylindrical body 11 is flexed in the elliptical shape, the diaphragm 12 bends back as indicated by the arrow in FIG. 3(b) about a base portion connected to the boss 13 in the cross-section that includes the major axis of the ellipse. In contrast, in the cross-section that includes the minor axis, the diaphragm 12 tilts toward the open end 11a as indicated by the arrow in FIG. 3(c). Therefore, while the diaphragm 12 is subjected to this type of flexural stress towards a central axis 11b, it is also subjected to shear stress due to torque transmission.
Therefore, with the diaphragm 12 under this combination of stresses, the cross-sectional shape thereof is designed so that only a small force is required to deform the part of the cylindrical body 11 on the side of the open end in an elliptical shape, and a large torque can be transmitted. In particular, the cross-sectional shape of the diaphragm is designed so that stress is not concentrated on the diaphragm when it is under this combination of stresses. A cup-shaped flexible external gear whereby stress concentration can be alleviated is disclosed in JP-A 6-17888, for example.
The amount of deformation of the diaphragm 12 towards the central axis 11b varies according to the reduction ratio of the wave gear device 1. In the case of a low reduction ratio, since there is a large amount of elliptical deformation in the cylindrical body 11 on the side of the open end, the amount of deformation of the diaphragm 12 in the direction of the central axis 11b increases by a commensurate amount. In contrast, the amount of deformation decreases when the reduction ratio is high. The optimum cross-sectional shape of the diaphragm 12 thus differs according to the reduction ratio. However, in the prior art, the cross-sectional shape of the diaphragm 12 is not determined with consideration for the reduction ratio, and the optimum cross-sectional shape of the diaphragm is determined based on the large amount of deformation of the diaphragm 12 in the central axis direction at a low reduction ratio.
Specifically, flexural stress occurring in conjunction with the elliptical deformation of the cylindrical body, shear stress caused by transmission torque, and flexural stress caused by assembly error basically act on the diaphragm of the flexible external gear of the wave gear device. However, in the case of the wave gear device having a high reduction ratio of 100 or higher, since the amount of elliptical deformation is small, the flexural stress caused thereby is also small, and the shear stress caused by transmission torque takes precedence.
In the conventional method for setting the cross-sectional shape of the diaphragm, the large flexural stress in the case of a low reduction ratio is assumed. As a result, a maximum allowable transmission torque is limited since an excessive allowable flexural stress is employed and an allowable shear stress is kept low when the cross-sectional shape of the diaphragm of the wave gear device with the high reduction ratio is set.